On the representability of the biuniform matroid
Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems i...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2014
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| Online Access: | https://hdl.handle.net/10356/101419 http://hdl.handle.net/10220/18666 |
| _version_ | 1811681084608348160 |
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| author | Ball, Simeon Padró, Carles Weiner, Zsuzsa Xing, Chaoping |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Ball, Simeon Padró, Carles Weiner, Zsuzsa Xing, Chaoping |
| author_sort | Ball, Simeon |
| collection | NTU |
| description | Every biuniform matroid is representable over all sufficiently large fields. But it is not
known exactly over which finite fields they are representable, and the existence of efficient methods
to find a representation for every given biuniform matroid has not been proved. The interest of these
problems is due to their implications to secret sharing. The existence of efficient methods to find
representations for all biuniform matroids is proved here for the first time. The previously known
efficient constructions apply only to a particular class of biuniform matroids, while the known general
constructions were not proved to be efficient. In addition, our constructions provide in many cases
representations over smaller finite fields. |
| first_indexed | 2024-10-01T03:35:19Z |
| format | Journal Article |
| id | ntu-10356/101419 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:35:19Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1014192023-02-28T19:41:32Z On the representability of the biuniform matroid Ball, Simeon Padró, Carles Weiner, Zsuzsa Xing, Chaoping School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Discrete mathematics Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields. Published version 2014-01-22T01:53:55Z 2019-12-06T20:38:27Z 2014-01-22T01:53:55Z 2019-12-06T20:38:27Z 2013 2013 Journal Article Ball, S., Padró, C., Weiner, Z., & Xing, C. (2013). On the representability of the biuniform matroid. SIAM journal on discrete mathematics, 27(3), 1482-1491. https://hdl.handle.net/10356/101419 http://hdl.handle.net/10220/18666 10.1137/120886960 en SIAM journal on discrete mathematics © 2013 Society for Industrial and Applied Mathematics (SIAM). This paper was published in SIAM Journal on Discrete Mathematics and is made available as an electronic reprint (preprint) with permission of SIAM. The paper can be found at the following official DOI: [http://dx.doi.org/10.1137/120886960]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Discrete mathematics Ball, Simeon Padró, Carles Weiner, Zsuzsa Xing, Chaoping On the representability of the biuniform matroid |
| title | On the representability of the biuniform matroid |
| title_full | On the representability of the biuniform matroid |
| title_fullStr | On the representability of the biuniform matroid |
| title_full_unstemmed | On the representability of the biuniform matroid |
| title_short | On the representability of the biuniform matroid |
| title_sort | on the representability of the biuniform matroid |
| topic | DRNTU::Science::Mathematics::Discrete mathematics |
| url | https://hdl.handle.net/10356/101419 http://hdl.handle.net/10220/18666 |
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